Curvature perturbation from symmetry breaking the end of inflation

Alabidi, Laila; Lyth, David H.

doi:10.1088/1475-7516/2006/08/006

Cited by 76 publications

(109 citation statements)

References 9 publications

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“…Typically, we will also find that the sourcing of curvature modes by isocurvature modes will be moderate, although this is not required; rather, weak sourcing (sin ∆ N ≪ 1) or strong sourcing (cos ∆ N ≪ 1) simply makes the bound in equation (60) even that much harder to satisfy. In other words, searching for scenarios where the sourcing is moderate maximizes the chance of finding scenarios that produce large non-Gaussianity.…”

Section: Conditions For Large |Fnl|mentioning

confidence: 97%

“…And more likely than not, the sourcing will be moderate, but this is not a requirement. Rather, if the total sourcing is tiny (sin ∆ N ≪ 1) or is very large (cos ∆ N ≪ 1), then the trigonometric terms will make it even that much harder to satisfy the bound in equation (60). Figure 1 illustrates this point by showing the value of the factor sin 2 ∆ N cos 2 ∆ N as a function of the total mode sourcing, T RS .…”

Section: A Calculation Of Fnl Using the δN Formalismmentioning

confidence: 99%

“…Indeed, there have been many attempts to calculate the level of non-Gaussianity in general multi-field models (e.g., [31][32][33][34][35][36][37][38][39][40][41][42]), as well as in two-field models (e.g., [43][44][45][46][47][48][49][50][51]). However, it has been very difficult to find models that produce large nonGaussianity, though some exceptions have been found such as in the curvaton model [52][53][54][55][56][57][58], hybrid and multibrid inflation (e.g., [59][60][61][62][63][64][65][66][67]), in certain modulated and tachyonic (p)re-heating scenarios (e.g., [68][69][70][71][72][73][74]), and in some quadratic small-field, two-field models by taking appropriate care of loop corrections [75,76]. Moreover, it has not been wholly clear why it is so diff...…”

Section: Introductionmentioning

confidence: 99%

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Non-Gaussianity in two-field inflation

2011

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We derive semi-analytic formulae for the local bispectrum and trispectrum in general two-field inflation and provide a simple geometric recipe for building observationally allowed models with observable non-Gaussianity. We use the δN formalism to express the bispectrum in terms of spectral observables and the transfer functions, which encode the super-horizon evolution of modes. Similarly, we calculate the trispectrum and show that the trispectrum parameter τNL can be expressed entirely in terms of spectral observables, which provides a new consistency relation unique to two-field inflation. We show that in order to generate observably large non-Gaussianity during inflation, the sourcing of curvature modes by isocurvature modes must be extremely sensitive to a change in the initial conditions orthogonal to the inflaton trajectory and that the amount of sourcing must be non-zero. Under some minimal assumptions, we argue that the first condition is satisfied only when neighboring trajectories through the two-dimensional field space diverge during inflation. Geometrically, this means that the inflaton must roll along a ridge in the potential V for some time during inflation and that its trajectory must turn somewhat in field space. Therefore, it follows that under our assumptions, two-field scenarios with attractor solutions necessarily produce small nonGaussianity. This explains why it has been so difficult to achieve large non-Gaussianity in two-field inflation, and why it has only been achieved in a narrow class of models where the potential and/or the initial conditions are fine-tuned. Some of our conclusions generalize at least qualitatively to multi-field inflation and to scenarios where the interplay between curvature and isocurvature modes can be represented by the transfer function formalism.

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Section: Conditions For Large |Fnl|mentioning

confidence: 97%

Section: A Calculation Of Fnl Using the δN Formalismmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Non-Gaussianity in two-field inflation

2011

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“…These consist of models in which both fields evolve during inflation, leading to a wide spectrum of possible behaviour [8][9][10][11][12][13][14][15][16][17][18]; curvaton-type behaviour which we define as the case where a second field begins to oscillate after the first field has reheated into radiation and its relative contribution to the energy density can gradually increase 2 [19][20][21][22][23][24][25] (also see Ref. [26,27]); and finally scenarios in which the process by which one (or both) of the fields reheat is directly dependent on the value of one of the light fields, which includes the scenarios known as Modulated Reheating (mr) [28][29][30][31][32][33][34][35] and the Inhomogeneous End of Inflation (iei) [36][37][38][39][40][41][42]. For reviews of these scenarios see Refs.…”

Section: Introductionmentioning

confidence: 99%

What Planck does not tell us about inflation

2013

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Planck data has not found the 'smoking gun' of non-Gaussianity that would have necessitated consideration of inflationary models beyond the simplest canonical single field scenarios. This raises the important question of what these results do imply for more general models, and in particular, multi-field inflation. In this paper we revisit four ways in which two-field scenarios can behave differently from single field models; two-field slow-roll dynamics, curvaton-type behaviour, inflation ending on an inhomogeneous hypersurface and modulated reheating. We study the constraints that Planck data puts on these classes of behaviour, focusing on the latter two which have been least studied in the recent literature. We show that these latter classes are almost equivalent, and extend their previous analyses by accounting for arbitrary evolution of the isocurvature mode which, in particular, places important limits on the Gaussian curvature of the reheating hypersurface. In general, however, we find that Planck bispectrum results only constrain certain regions of parameter space, leading us to conclude that inflation sourced by more than one scalar field remains an important possibility.

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“…depends not only on the inflaton but also on another light field σ, the critical value φ cr also fluctuates, which leads to the perturbation of the duration of the inflation, that is, δN [29][30][31][32][33].…”

Section: Inhomogeneous End Of Hybrid Inflationmentioning

confidence: 99%

Implications of Planck results for models with local type non-Gaussianity

Suyama

Takahashi

Yamaguchi

et al. 2013

J. Cosmol. Astropart. Phys.

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We discuss implications of Planck results for models with local type non-Gaussianity. In light of the recent results of the Planck satellite, we constrain model parameters of several representative models and give the prediction of trispectrum, in particular, g NL . We also consider interesting possibilities that trispectrum appears as the first signature of the non-Gaussianities of the curvature perturbations, that is, f NL is small while g NL can be significantly large.

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Curvature perturbation from symmetry breaking the end of inflation

Abstract: We consider a two-field hybrid inflation model, in which the curvature perturbation is predominantly generated at the end of inflation. By finely tuning the coupling of the fields to the waterfall we find that we can get a measurable amount of non-gaussianity.

Cited by 76 publications

References 9 publications

Non-Gaussianity in two-field inflation

Non-Gaussianity in two-field inflation

What Planck does not tell us about inflation

Implications of Planck results for models with local type non-Gaussianity

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